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Proof step 52 from proof pathexplus-pathex (previous step)

validrefs(str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st) ⊦ refs1 = [], r = (r ' + refs1) .last, ∃ refs. refs ≠ [] ∧ refs .first = r ∧ validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st) ∧ step∃(str, refs .last, (refs .first ' + refs1) .last, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
validrefs(str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st) ⊦ refs1 = [], r = refs1 .last, ∃ refs. refs ≠ [] ∧ refs .first = r ∧ validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st) ∧ step∃(str, refs .last, refs1 .last, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refs ≠ [] → (r ' + refs) .last = refs .last])]]